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The Heterogeneous Vehicle–Routing Game

Department of Mathematics, Linköping Institute of Technology, 581 83 Linköping, Stockholm, Sweden
Department of Mathematics, Linköping Institute of Technology, 581 83 Linköping, Stockholm, Sweden
Department of Science and Technology, Linköping Institute of Technology, 601 74 Norrköping, Stockholm, Sweden
steng{at}mai.liu.se
mabre{at}mai.liu.se
petva{at}itn.liu.se

In this paper, we study a cost–allocation problem that arises in a distribution–planning situation at the Logistics Department at Norsk Hydro Olje AB, Stockholm, Sweden. We consider the routes from one depot during one day. The total distribution cost for these routes is to be divided among the customers that are visited. This cost–allocation problem is formulated as a vehicle–routing game (VRG), allowing the use of vehicles with different capacities. Cost–allocation methods based on different concepts from cooperative game theory, such as the core and the nucleolus, are discussed. A procedure that can be used to investigate whether the core is empty or not is presented, as well as a procedure to compute the nucleolus. Computational results for the Norsk Hydro case are presented and discussed.

Key Words: vehicle routing; heterogeneous vehicles; cooperative game theory; cost allocation; generalized multiple tour problem
History: Received: December 2000; revised: September 2001; revised: February 2003; accepted: February 2003.

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